When you’re feeling things in such a way that they seem to be “on top of you,” they’re addosso, like in this Lorenzo Jovanotti song.
Summer [is] upon us
Un anno è già passato
A year has already gone by
He’s talking about the summer season, but also the weight (and heat) of summer. We might even say he feels it on his shoulders or back. Addosso can mean on top, right nearby, but definitely close (in time or space), close enough to be breathing down your neck. It can even be so close as to be inside you.
This somewhat peculiar word has a little history. Dosso is a rather archaic way of saying dorso (back, spine). Remembering this will help in assimilating addosso and di dosso (off of). As a noun, dosso by itself is used when talking about geological formations (bumps or hills), or in la segnaletica stradale (road signs) to indicate a bump or a rise.
Dosso usually gets together with a preposition to be transformed into a compound preposition/adverb: addosso. If there’s an indirect object in the form of a noun, as in the following example, we need the preposition a (to).
Il ramo è caduto addosso ad un bambino.
The branch fell onto a child.
If we use an object pronoun, we have:
Il ramo è caduto addosso a lui.
The branch fell onto him.
To make the sentence flow better, we can turn it around, employing the famous combination: indirect object pronoun + preposition (if this is unfamiliar to you, see Ci Gets Around: Part 1 and Ricordare: Remembering and Reminding). A lui (to him) becomes gli (to him):
Gli [a lui] è caduto il ramo addosso.
The branch fell on top of him.
In this case, we generally find addosso at the end of the sentence or clause, and the object pronoun will be elsewhere.
Eh sì. Infatti, lui ci ha rovesciato tutto il vassoio addosso.
Oh yes. In fact, he even spilled the contents of the tray on top of us.
Caption 36, Anna e Marika - Il verbo essere - Part 1Play Caption
Di dosso (from your back, off your back), usually used with a word meaning “to remove” such as togliere or levare:
Me lo sono levato di dosso.
I got it off my back [I got rid of it].
Toglimi le mani di dosso.
Take your hands off me.
Addossare isn’t very common in normal conversation, but means something along the lines of “to lean.” It’s used when talking about blame or responsibility:
addossare la colpa
to lay the blame
addossarsi la responsabilità
to take responsibility
Indossare (to wear, to put on, literally “to put on one’s back”):
Indossava una sciarpa rossa.
She was wearing a red scarf.
In a nutshell:
When referring to “on,” we use addosso
When referring to “off,” we use di dosso
Addosso will need the preposition a (to), which may be hidden in the object pronoun.
Di dosso, on the other hand, already has its (detached) preposition: di (of).
The most common related verb form is indossare (to wear).
A Yabla video search of addosso will give you some good examples of how it’s used.
Just for fun:
Stavo facendo un giro in bicicletta. Indossavo una maglia colorata, e quindi ero ben visibile, ma nonostante ciò, una macchina mi è venuta proprio addosso e sono cascato. Poi la bici stessa mi è cascata addosso. Non sono riuscito subito a togliermela di dosso. L’autista non mi ha aiutato e neanche voleva addossarsi la responsabilità. Ogni tanto, questa cattiva esperienza me la sento ancora addosso.
I was taking a bike ride. I was wearing a bright jersey, and so I was quite visible, but in spite of that, a car bumped right into me and I fell off. Then the bike itself fell onto me. I wasn’t able to get it off me right away. The driver didn’t help me, nor did he want to take responsibility. Every now and then, I still feel this bad experience inside of me.